Can some help me with this appendix please. Thank you
Pay attention to the units of measure. You may have to convert from feet to miles several times in this assignment. You can use 1 mile = 5,280 feet for your conversions.
1. Many people know that the weight of an object varies on different planets, but did you know that the weight of an object on Earth also varies according to the elevation of the object? In particular, the weight of an object follows this equation: , where C is a constant, and r is the distance that the object is from the center of Earth.
a. Solve the equation for r.
b. Suppose that an object is 100 pounds when it is at sea level. Find the value of C that makes the equation true. (Sea level is 3,963 miles from the center of the Earth.)
c. Use the value of C you found in the previous question to determine how much the object would weigh in
i. Death Valley (282 feet below sea level).
ii. the top of Mount McKinley (20,320 feet above sea level).
I can't answer this question because I need help with this myself.
To solve this problem, we need to follow these steps:
Step 1: Solve the equation for r.
The equation is given as:
Weight = C / r
To solve for r, we need to isolate it on one side of the equation.
Dividing both sides of the equation by Weight, we get:
1 / Weight = C / r
To isolate r, we can take the reciprocal of both sides:
r / C = Weight
Finally, we can multiply both sides of the equation by C to solve for r:
r = C / Weight
Step 2: Find the value of C that makes the equation true.
We are given that the weight of the object at sea level is 100 pounds (Weight = 100). Sea level is 3,963 miles from the center of the Earth. Substituting these values into the equation, we get:
3,963 = C / 100
To find C, we can multiply both sides of the equation by 100:
C = 3,963 * 100
C = 396,300
So the value of C that makes the equation true is 396,300.
Step 3: Use the value of C to determine the weight of the object at different locations.
Now that we have the value of C, we can use it to calculate the weight of the object in different locations.
i. Death Valley (282 feet below sea level):
To calculate the weight, we need to convert the distance from feet to miles.
282 feet / 5,280 feet per mile = 0.053 miles
Using the equation with the value of C and r = -0.053 miles (negative because it is below sea level):
Weight (Death Valley) = C / r
Weight (Death Valley) = 396,300 / (-0.053)
Weight (Death Valley) = -7,480,189 pounds (approximately)
ii. The top of Mount McKinley (20,320 feet above sea level):
Similar to the previous calculation, we convert the distance from feet to miles:
20,320 feet / 5,280 feet per mile = 3.85 miles
Using the equation with the value of C and r = 3.85 miles:
Weight (Mount McKinley) = C / r
Weight (Mount McKinley) = 396,300 / 3.85
Weight (Mount McKinley) = 102,857 pounds (approximately)
Therefore, the weight of the object in Death Valley would be approximately -7,480,189 pounds, and the weight of the object at the top of Mount McKinley would be approximately 102,857 pounds.